Do you ever feel that your students don’t seem to know the pre-requisite math for your classes, even though they did well in their math classes? Math in physics is different from pure math and learning that can be challenging for students. They have to learn to develop physical concepts and blend them with symbolic math.¹ This is harder than you might think.

In my 8 short articles in The Physics Teacher,² I identify 7 tools students need to learn to build the blend — dimensional analysis, estimation, anchor equations (reading the physics in an equation), toy models, functional dependence, reading the physics in a graph, and telling the story. I explain both why these are so important and why so many students have difficulty with them in physics.

In each article, I suggest a variety of instructional methods you can use to help students learn to use these tools, and, as a result, develop a strong physical intuition and learn to “think with math”. The supplementary materials for each article and the associated submissions to the Living Physics Portal³ offer lots of relevant problems you can use in class and for homework.

The column "Physics Challenges for Teachers and Students" published hundreds of braintwisters and reader-submitted solutions at TPT between 2000 and 2023. The solutions came from all over the world, and it was a pleasure to interact with so many problem-solving enthusiasts from every continent. In my talk, I will discuss the history of the column, my favorite problems, and the TPT articles inspired by some of the problems. The most prolific and successful solvers can expect personal shoutouts. 

In addition, I will discuss the role of problem-solving in high-school and undergraduate physics classes.